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C₄×#117×C₅₉ #21420588

order	7552
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₅₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

C₄×#117×C₅₉

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₅₉	C₂²
commutator	C₂	C₂²×C₄²×C₅₉
Frattini, cosocle	C₂³	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₂⁴
prime radical	C₂⁴×C₅₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₅₉ ◁ G

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4720 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28478088, #28478094, #28478128, …
maximal subgroup of	C₅₉×#7854, C₅₉×#7856, C₅₉×#7866, …
maximal normal subgroup of	C₅₉×#7854, C₅₉×#7856, C₅₉×#7866, …
maximal quotient of	C₄×C₅₉×#376, C₄²×C₂²⋊C₄×C₅₉, C₄²×C₄⋊C₄×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 1002);